Tricky Math

Pablo buys a horse for $10,000, sells it again for $12,000, buys it again for $14,000, and finally sells it again for $16,000. Did Pablo make a profit or a loss, and if so, how much of one?

Got an answer? Now, stop reading and think over it again, just to be sure :D.

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Done? Good! The thing is, Tim Gowers in his blog told a story about an experiment on Math teachers in Latin America in which those teachers were asked the above question. Guess what, only a small percentage of their answers are correct :D. Two common wrong answers are as follows.

1. Pablo bought the horse for $10,000 and sold it for $12,000, making a profit of $2,000. But then he bought it again for $14,000, so he made a loss of $2,000. Finally, he sold it for $16,000, making a profit of $2,000. Adding up the profits and loss you get $2,000.

2. Pablo started off buying the horse for $10,000 and ended up selling it for $16,000 so at the end of the whole process he had made a profit of $6,000.

The correct answer is $4000 [Hint: Think of how much he paid totally, and how much he got totally]. Amusingly, even given a very clear explanation, those Math teachers still didn’t get the answer (see Gower’s post for more details).